Results obtained using Gurobi for solving a nonlinear Facility Location Problem (FLP), using the models described in Mathematical Optimization: Solving Problems using Python and Gurobi.
Parameters used: number of facilities is 10% of the number of customers.
CPU time limited to 300 seconds. (Click on values for selecting data to display.)Instance family | Type | Description |
Num.Int=2 | random | Number of linear segments in the approximation: 2 |
Num.Int=5 | random | Number of linear segments in the approximation: 5 |
Num.Int=10 | random | Number of linear segments in the approximation: 10 |
Num.Int=20 | random | Number of linear segments in the approximation: 20 |
Num.Int=50 | random | Number of linear segments in the approximation: 50 |
Num.Int=100 | random | Number of linear segments in the approximation: 100 |
Num.Int=200 | random | Number of linear segments in the approximation: 200 |
Num.Int=500 | random | Number of linear segments in the approximation: 500 |
Num.Int=1000 | random | Number of linear segments in the approximation: 1000 |
Label | Description |
mselect | multiple selection model |
cc_dis | disaggregated convex combination model |
cc_dis_log | disaggregated convex combination model with a logarithmic number of variables |
cc_agg | (aggregated) convex combination model |
cc_agg_log | (aggregated) convex combination model with a logarithmic number of variables |
sos | model using sos constraints of type 2 |
size | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
20 | 0.00 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 |
50 | 0.02 | 0.02 | 0.02 | 0.03 | 0.02 | 0.01 |
100 | 0.07 | 0.07 | 0.06 | 0.10 | 0.04 | 0.02 |
200 | 0.39 | 0.33 | 0.24 | 0.25 | 0.21 | 0.08 |
500 | 4.75 | 5.46 | 2.80 | 2.87 | 2.32 | 1.03 |
1000 | 20.96 | 49.64 | 21.05 | 23.49 | 22.10 | 15.25 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 |
2 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
3 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 |
5 | 0.00 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
7 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
8 | 0.00 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 |
9 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.02 | 0.01 | 0.01 | 0.01 | 0.00 |
1 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 |
2 | 0.01 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 |
3 | 0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 |
4 | 0.00 | 0.01 | 0.02 | 0.00 | 0.01 | 0.01 |
5 | 0.00 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 |
6 | 0.01 | 0.01 | 0.01 | 0.00 | 0.02 | 0.00 |
7 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 |
8 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 |
9 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.01 | 0.00 | 0.01 | 0.01 | 0.01 |
1 | 0.02 | 0.01 | 0.02 | 0.01 | 0.01 | 0.00 |
2 | 0.03 | 0.04 | 0.02 | 0.03 | 0.03 | 0.01 |
3 | 0.03 | 0.02 | 0.01 | 0.05 | 0.03 | 0.01 |
4 | 0.02 | 0.03 | 0.03 | 0.04 | 0.03 | 0.00 |
5 | 0.02 | 0.02 | 0.02 | 0.06 | 0.03 | 0.01 |
6 | 0.01 | 0.02 | 0.03 | 0.01 | 0.01 | 0.01 |
7 | 0.01 | 0.04 | 0.04 | 0.01 | 0.01 | 0.01 |
8 | 0.01 | 0.02 | 0.02 | 0.02 | 0.01 | 0.01 |
9 | 0.02 | 0.03 | 0.02 | 0.05 | 0.01 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.02 | 0.02 | 0.01 | 0.02 | 0.01 | 0.01 |
1 | 0.07 | 0.10 | 0.08 | 0.15 | 0.05 | 0.02 |
2 | 0.11 | 0.07 | 0.09 | 0.11 | 0.05 | 0.01 |
3 | 0.06 | 0.06 | 0.07 | 0.09 | 0.04 | 0.03 |
4 | 0.09 | 0.13 | 0.12 | 0.09 | 0.09 | 0.02 |
5 | 0.09 | 0.08 | 0.07 | 0.08 | 0.04 | 0.02 |
6 | 0.04 | 0.04 | 0.04 | 0.12 | 0.04 | 0.02 |
7 | 0.12 | 0.08 | 0.06 | 0.17 | 0.04 | 0.01 |
8 | 0.05 | 0.05 | 0.04 | 0.06 | 0.04 | 0.03 |
9 | 0.08 | 0.05 | 0.05 | 0.16 | 0.04 | 0.03 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.43 | 0.45 | 0.35 | 0.33 | 0.30 | 0.08 |
1 | 0.39 | 0.24 | 0.17 | 0.20 | 0.12 | 0.07 |
2 | 0.58 | 0.64 | 0.20 | 0.25 | 0.17 | 0.09 |
3 | 0.47 | 0.37 | 0.25 | 0.26 | 0.21 | 0.09 |
4 | 0.49 | 0.48 | 0.27 | 0.23 | 0.25 | 0.10 |
5 | 0.23 | 0.28 | 0.15 | 0.23 | 0.17 | 0.06 |
6 | 0.59 | 0.25 | 0.34 | 0.24 | 0.32 | 0.08 |
7 | 0.22 | 0.23 | 0.18 | 0.27 | 0.17 | 0.06 |
8 | 0.19 | 0.16 | 0.14 | 0.26 | 0.12 | 0.06 |
9 | 0.34 | 0.24 | 0.35 | 0.22 | 0.29 | 0.11 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 2.01 | 2.95 | 2.11 | 3.06 | 2.23 | 1.32 |
1 | 2.78 | 6.89 | 2.98 | 2.72 | 2.47 | 1.29 |
2 | 2.39 | 3.42 | 2.70 | 2.81 | 2.55 | 1.26 |
3 | 2.15 | 2.62 | 1.65 | 2.24 | 2.15 | 0.91 |
4 | 4.03 | 6.86 | 3.18 | 3.35 | 3.55 | 0.78 |
5 | 0.80 | 0.77 | 0.72 | 1.37 | 0.57 | 0.42 |
6 | 1.97 | 2.70 | 2.85 | 3.08 | 2.64 | 0.88 |
7 | 22.15 | 19.05 | 6.06 | 4.86 | 3.11 | 1.80 |
8 | 7.37 | 6.03 | 4.48 | 3.95 | 2.95 | 1.12 |
9 | 1.82 | 3.31 | 1.28 | 1.27 | 0.97 | 0.49 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 56.44 | 145.44 | 28.90 | 21.93 | 26.59 | 36.76 |
1 | 19.91 | 62.30 | 16.39 | 17.34 | 16.17 | 10.57 |
2 | 31.44 | 89.51 | 33.01 | 25.26 | 34.60 | 19.87 |
3 | 16.34 | 30.93 | 24.58 | 29.19 | 33.33 | 20.90 |
4 | 8.82 | 10.21 | 8.70 | 16.01 | 12.96 | 5.58 |
5 | 17.32 | 85.10 | 34.10 | 58.15 | 36.84 | 12.87 |
6 | 19.73 | 22.97 | 25.31 | 21.82 | 14.16 | 8.23 |
7 | 8.29 | 10.30 | 15.38 | 14.67 | 17.10 | 7.33 |
8 | 25.21 | 34.39 | 18.68 | 24.56 | 19.48 | 24.73 |
9 | 6.14 | 5.22 | 5.41 | 5.97 | 9.80 | 5.64 |